X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/41a324a748544b0fb9b0acfc65b1a39b7611550c..02dfbd5b7af7816959dbd39c1fe628451204e35f:/ec.c

diff --git a/ec.c b/ec.c
index 37d8ad3..e5e1c87 100644
--- a/ec.c
+++ b/ec.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: ec.c,v 1.2 2001/05/07 17:29:44 mdw Exp $
+ * $Id$
  *
  * Elliptic curve definitions
  *
@@ -27,35 +27,40 @@
  * MA 02111-1307, USA.
  */
 
-/*----- Revision history --------------------------------------------------* 
- *
- * $Log: ec.c,v $
- * Revision 1.2  2001/05/07 17:29:44  mdw
- * Treat projective coordinates as an internal representation.  Various
- * minor interface changes.
- *
- * Revision 1.1  2001/04/29 18:12:33  mdw
- * Prototype version.
- *
- */
-
 /*----- Header files ------------------------------------------------------*/
 
 #include "ec.h"
 
 /*----- Trivial wrappers --------------------------------------------------*/
 
+/* --- @ec_samep@ --- *
+ *
+ * Arguments:	@ec_curve *c, *d@ = two elliptic curves
+ *
+ * Returns:	Nonzero if the curves are identical (not just isomorphic).
+ *
+ * Use:		Checks for sameness of curves.  This function does the full
+ *		check, not just the curve-type-specific check done by the
+ *		@sampep@ field operation.
+ */
+
+int ec_samep(ec_curve *c, ec_curve *d)
+{
+  return (c == d || (field_samep(c->f, d->f) &&
+		     c->ops == d->ops && EC_SAMEP(c, d)));
+}
+
 /* --- @ec_create@ --- *
  *
  * Arguments:	@ec *p@ = pointer to an elliptic-curve point
  *
- * Returns:	---
+ * Returns:	The argument @p@.
  *
  * Use:		Initializes a new point.  The initial value is the additive
  *		identity (which is universal for all curves).
  */
 
-void ec_create(ec *p) { EC_CREATE(p); }
+ec *ec_create(ec *p) { EC_CREATE(p); return (p); }
 
 /* --- @ec_destroy@ --- *
  *
@@ -82,28 +87,50 @@ int ec_atinf(const ec *p) { return (EC_ATINF(p)); }
  *
  * Arguments:	@ec *p@ = pointer to a point
  *
- * Returns:	---
+ * Returns:	The argument @p@.
  *
  * Use:		Sets the given point to be the point %$O$% at infinity.
  */
 
-void ec_setinf(ec *p) { EC_SETINF(p); }
+ec *ec_setinf(ec *p) { EC_SETINF(p); return (p); }
 
 /* --- @ec_copy@ --- *
  *
  * Arguments:	@ec *d@ = pointer to destination point
  *		@const ec *p@ = pointer to source point
  *
- * Returns:	---
+ * Returns:	The destination @d@.
  *
  * Use:		Creates a copy of an elliptic curve point.
  */
 
-void ec_copy(ec *d, const ec *p) { EC_COPY(d, p); }
+ec *ec_copy(ec *d, const ec *p) { EC_COPY(d, p); return (d); }
+
+/* --- @ec_eq@ --- *
+ *
+ * Arguments:	@const ec *p, *q@ = two points
+ *
+ * Returns:	Nonzero if the points are equal.  Compares external-format
+ *		points.
+ */
+
+int ec_eq(const ec *p, const ec *q) { return (EC_EQ(p, q)); }
 
 /*----- Standard curve operations -----------------------------------------*/
 
-/* --- @ec_idin@, @ec_idout@ --- *
+/* --- @ec_stdsamep@ --- *
+ *
+ * Arguments:	@ec_curve *c, *d@ = two elliptic curves
+ *
+ * Returns:	Nonzero if the curves are identical (not just isomorphic).
+ *
+ * Use:		Simple sameness check on @a@ and @b@ curve members.
+ */
+
+int ec_stdsamep(ec_curve *c, ec_curve *d)
+  { return (MP_EQ(c->a, d->a) && MP_EQ(c->b, d->b)); }
+
+/* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- *
  *
  * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
  *		@ec *d@ = pointer to the destination
@@ -142,7 +169,10 @@ ec *ec_idout(ec_curve *c, ec *d, const ec *p)
   return (d);
 }
 
-/* --- @ec_projin@, @ec_projout@ --- *
+ec *ec_idfix(ec_curve *c, ec *d, const ec *p)
+  { EC_COPY(d, p); return (d); }
+
+/* --- @ec_projin@, @ec_projout@, @ec_projfix@ --- *
  *
  * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
  *		@ec *d@ = pointer to the destination
@@ -172,20 +202,86 @@ ec *ec_projout(ec_curve *c, ec *d, const ec *p)
   if (EC_ATINF(p))
     EC_SETINF(d);
   else {
-    mp *x, *y, *z;
+    mp *x, *y, *z, *zz;
+    field *f = c->f;
+    if (p->z == f->one) {
+      d->x = F_OUT(f, d->x, p->x);
+      d->y = F_OUT(f, d->y, p->y);
+    } else {
+      z = F_INV(f, MP_NEW, p->z);
+      zz = F_SQR(f, MP_NEW, z);
+      z = F_MUL(f, z, zz, z);
+      x = F_MUL(f, d->x, p->x, zz);
+      y = F_MUL(f, d->y, p->y, z);
+      mp_drop(z);
+      mp_drop(zz);
+      d->x = F_OUT(f, x, x);
+      d->y = F_OUT(f, y, y);
+    }
+    mp_drop(d->z);
+    d->z = 0;
+  }
+  return (d);
+}
+
+ec *ec_projfix(ec_curve *c, ec *d, const ec *p)
+{
+  if (EC_ATINF(p))
+    EC_SETINF(d);
+  else if (p->z == c->f->one)
+    EC_COPY(d, p);
+  else {
+    mp *z, *zz;
     field *f = c->f;
     z = F_INV(f, MP_NEW, p->z);
-    x = F_MUL(f, d->x, p->x, z);
-    y = F_MUL(f, d->y, p->y, z);
+    zz = F_SQR(f, MP_NEW, z);
+    z = F_MUL(f, z, zz, z);
+    d->x = F_MUL(f, d->x, p->x, zz);
+    d->y = F_MUL(f, d->y, p->y, z);
     mp_drop(z);
+    mp_drop(zz);
     mp_drop(d->z);
-    d->x = F_OUT(f, x, x);
-    d->y = F_OUT(f, y, y);
-    d->z = 0;
+    d->z = MP_COPY(f->one);
   }
   return (d);
 }
 
+/* --- @ec_stdsub@ --- *
+ *
+ * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
+ *		@ec *d@ = pointer to the destination
+ *		@const ec *p, *q@ = the operand points
+ *
+ * Returns:	The destination @d@.
+ *
+ * Use:		Standard point subtraction operation, in terms of negation
+ *		and addition.  This isn't as efficient as a ready-made
+ *		subtraction operator.
+ */
+
+ec *ec_stdsub(ec_curve *c, ec *d, const ec *p, const ec *q)
+{
+  ec t = EC_INIT;
+  EC_NEG(c, &t, q);
+  EC_FIX(c, &t, &t);
+  EC_ADD(c, d, p, &t);
+  EC_DESTROY(&t);
+  return (d);
+}
+
+/*----- Creating curves ---------------------------------------------------*/
+
+/* --- @ec_destroycurve@ --- *
+ *
+ * Arguments:	@ec_curve *c@ = pointer to an ellptic curve
+ *
+ * Returns:	---
+ *
+ * Use:		Destroys a description of an elliptic curve.
+ */
+
+void ec_destroycurve(ec_curve *c) { c->ops->destroy(c); }
+
 /*----- Real arithmetic ---------------------------------------------------*/
 
 /* --- @ec_find@ --- *
@@ -204,10 +300,24 @@ ec *ec_find(ec_curve *c, ec *d, mp *x)
   x = F_IN(c->f, MP_NEW, x);
   if ((d = EC_FIND(c, d, x)) != 0)
     EC_OUT(c, d, d);
-  mp_drop(x);
+  MP_DROP(x);
   return (d);
 }
 
+/* --- @ec_neg@ --- *
+ *
+ * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
+ *		@ec *d@ = pointer to the destination point
+ *		@const ec *p@ = pointer to the operand point
+ *
+ * Returns:	The destination point.
+ *
+ * Use:		Computes the negation of the given point.
+ */
+
+ec *ec_neg(ec_curve *c, ec *d, const ec *p)
+  { EC_IN(c, d, p); EC_NEG(c, d, d); return (EC_OUT(c, d, d)); }
+
 /* --- @ec_add@ --- *
  *
  * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
@@ -231,6 +341,29 @@ ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q)
   return (d);
 }
 
+/* --- @ec_sub@ --- *
+ *
+ * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
+ *		@ec *d@ = pointer to the destination point
+ *		@const ec *p, *q@ = pointers to the operand points
+ *
+ * Returns:	The destination @d@.
+ *
+ * Use:		Subtracts one point from another on an elliptic curve.
+ */
+
+ec *ec_sub(ec_curve *c, ec *d, const ec *p, const ec *q)
+{
+  ec pp = EC_INIT, qq = EC_INIT;
+  EC_IN(c, &pp, p);
+  EC_IN(c, &qq, q);
+  EC_SUB(c, d, &pp, &qq);
+  EC_OUT(c, d, d);
+  EC_DESTROY(&pp);
+  EC_DESTROY(&qq);
+  return (d);
+}
+
 /* --- @ec_dbl@ --- *
  *
  * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
@@ -243,72 +376,49 @@ ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q)
  */
 
 ec *ec_dbl(ec_curve *c, ec *d, const ec *p)
-{
-  EC_IN(c, d, p);
-  EC_DBL(c, d, d);
-  return (EC_OUT(c, d, d));
-}
+  { EC_IN(c, d, p); EC_DBL(c, d, d); return (EC_OUT(c, d, d)); }
 
-/* --- @ec_mul@ --- *
+/* --- @ec_check@ --- *
  *
  * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
- *		@ec *d@ = pointer to the destination point
- *		@const ec *p@ = pointer to the generator point
- *		@mp *n@ = integer multiplier
+ *		@const ec *p@ = pointer to the point
  *
- * Returns:	---
+ * Returns:	Zero if OK, nonzero if this is an invalid point.
  *
- * Use:		Multiplies a point by a scalar, returning %$n p$%.
+ * Use:		Checks that a point is actually on an elliptic curve.
  */
 
-ec *ec_mul(ec_curve *c, ec *d, const ec *p, mp *n)
+int ec_check(ec_curve *c, const ec *p)
 {
-  mpscan sc;
-  ec g = EC_INIT;
-  unsigned sq = 0;
+  ec t = EC_INIT;
+  int rc;
 
-  EC_SETINF(d);
   if (EC_ATINF(p))
-    return;
-
-  mp_rscan(&sc, n);
-  if (!MP_RSTEP(&sc))
-    goto exit;
-  while (!MP_RBIT(&sc))
-    MP_RSTEP(&sc);
-
-  EC_IN(c, &g, p);
-  if ((n->f & MP_BURN) && !(g.x->f & MP_BURN))
-    MP_DEST(g.x, 0, MP_BURN);
-  if ((n->f & MP_BURN) && !(g.y->f & MP_BURN))
-    MP_DEST(g.y, 0, MP_BURN);
-
-  for (;;) {
-    EC_ADD(c, d, d, &g);
-    sq = 0;
-    for (;;) {
-      if (!MP_RSTEP(&sc))
-	goto done;
-      if (MP_RBIT(&sc))
-	break;
-      sq++;
-    }
-    sq++;
-    while (sq) {
-      EC_DBL(c, d, d);
-      sq--;
-    }
-  }
+    return (0);
+  EC_IN(c, &t, p);
+  rc = EC_CHECK(c, &t);
+  EC_DESTROY(&t);
+  return (rc);
+}
 
-done:
-  while (sq) {
-    EC_DBL(c, d, d);
-    sq--;
-  }
+/* --- @ec_rand@ --- *
+ *
+ * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
+ *		@ec *d@ = pointer to the destination point
+ *		@grand *r@ = random number source
+ *
+ * Returns:	The destination @d@.
+ *
+ * Use:		Finds a random point on the given curve.
+ */
 
-  EC_DESTROY(&g);
-exit:
-  return (EC_OUT(c, d, d));
+ec *ec_rand(ec_curve *c, ec *d, grand *r)
+{
+  mp *x = MP_NEW;
+  do x = F_RAND(c->f, x, r); while (!EC_FIND(c, d, x));
+  mp_drop(x);
+  if (grand_range(r, 2)) EC_NEG(c, d, d);
+  return (EC_OUT(c, d, d));    
 }
 
 /*----- That's all, folks -------------------------------------------------*/